Partition Functions, Duality, and the Tube Metric

TL;DR

This paper computes partition functions for type II strings on specific backgrounds, revealing connections between conformal field theories and non-perturbative fivebrane vacua in six dimensions.

Contribution

It explicitly calculates modular invariant partition functions for type II strings on R^6xK3 and W4, linking perturbative spectra to non-perturbative fivebrane vacua.

Findings

Partition functions are modular invariant sums over spin structures.

The theories probe non-perturbative vacua via conformal field theory.

A new D=6, N=(1,1) free fermion string model with distinct vacua.

Abstract

The partition function of type IIA and B strings on R^6xK3, in the T^4/Z_2 orbifold limit, is explicitly computed as a modular invariant sum over spin strutures required by perturbative unitarity in order to extend the analysis to include type II strings on R^6 x W4, where W4 is associated with the tube metric conformal field theory, given by the degrees of freedom transverse to the Neveu-Schwarz fivebrane solution. This generates partition functions and perturbative spectra of string theories in six space-time dimensions, associated with the modular invariants of the level k affine SU(2) Kac-Moody algebra. These theories provide a conformal field theory (i.e. perturbative) probe of non-perturbative (fivebrane) vacua. We contrast them with theories whose N=(4,4) sigma-model action contains n_H=k+2 hypermultiplets as well as vector supermultiplets, and where k is the level just mentioned. In Appendix B we also give a D=6, N=(1,1) `free fermion' string model which has a different moduli space of vacua from the 81 parameter space relevant to the above examples.